Discriminant analysis is a collection of statistical methods which has found important applications in medical diagnosis and prognosis, in management of health care units, and in medical research. Unfortunately, the diversity of types of medical data encountered makes it impossible to recommend one specific discriminant analysis procedure. The objective of this investigation is to create robust discrimination procedures which will yield low probabilities of misclassification for a wide variety of types of populations. To accomplish this objective we will develop new adaptive and nonparametric discrimination methods and will compare them with existing procedures for many different populations, using both real and simulated data. Adaptive procedures will be created which synthesize the various discrimination procedures by providing quantitative measures that can be used in real medical situations to indicate which discriminant procedure is recommended in each case.